
Instructor  Dominique Unruh 
TA  RaulMartin Rebane (submit homework solutions here) 
Lecture Period  February 6  May 23 
Lectures  Mondays, 12:1513:45, Δ1022
(Dominique; may sometimes be switched with tutorial) 
Practice sessions 
Tuesdays, 10:1512:00, Δ2045 (RaulMartin) 
Chat  https://zulip.cs.ut.ee/#narrow/stream/312QuantumCryptography2023 
Course Material  Lecture
notes, recordings, blackboard photos, and exam study guide. 
Language  English 
Exam  20230525, 10:00–13:00, Delta room 1008 
Contact  Dominique Unruh <<surname>at ut dot ee> 
Date  Summary  Knowlets covered  Materials 

Feb 06  General intro. Quantum systems, quantum states  QState  Video, Whiteboard 
Feb 07  Unitary operations, measurements in computational basis, ElitzurVaidman bomb tester  UniTrafo, CBMeas, PauliX, PauliY, PauliZ, Bomb  Video, Whiteboard 
Feb 13  Complete measurements. Projective measurements (subspace view).  ComplMeas, ProjMeasVS, Hada  Video, Whiteboard 
Feb 14  Quantum Zeno effect, polarization invariant under rotation.  ComplMeas, ConjTrans, Dirac  Whiteboard 
Feb 20  Projective measurements (projector view). Tensor product. Composition of quantum systems / quantum states / unitaries / measurements.  ProjMeas, ComposQSys, ComposQState, Tensor, ComposUni, ComposMeas  Video, Whiteboard 
Feb 21  Using tensor product and proj. measurements. Quantum teleportation  ProjMeas, Tensor, ComposUni, ComposMeas, CNOT, Hada  Whiteboard 
Feb 27  Quantum state probability distributions (ensembles). Operations on quantum state probability distributions. Density operators. Operations on density operators. Theorem: Physically indistinsuishable iff same density operator.  QDistr, PhysInd, QDistrU, QDistrX, QDistrM, Density, Density, DensityU, DensityM, DensityX, DensityPhysInd  Video, Whiteboard 
Feb 28  Density operators. Implementing boolean unitaries  QDistr, QDistrM, Density, DensityPhysInd, Toff  Whiteboard 
Mar 06  Quantum OneTime Pad. Partial Trace.  QOTP, ParTr  Video, Whiteboard 
Mar 07  Backwards toy crypto. Calculating Partial Trace. Tracing out buffer qubits in $U_f$. Impossibility of FTL communication.  ParTr  Whiteboard 
Mar 13  Motivation for trace distance. Statistical distance. Trace distance. Quantum operations.  SD, SDSumDef, SDProps, TD, TDMaxDef, TDSD, TDProps, QOper, QOperAlt  Video, Whiteboard 
Mar 14  Trace Distance of lecture example. QOTP with no zerokeys. Replace as Kraus operator. Trace Distance between arbitrary states.  QOper, ParTr, SD, SDSumDef  Whiteboard 
Mar 20  Quantum key distribution: Intro. Security definition. Protocol overview.  QKDIntro, QKDSecDef, QKDProto  Video, Whiteboard 
Mar 21  Prob. of measuring key after QKD. Alternate sec def of QKD. SMT from QKD.  QKDSecDef  Whiteboard 
Mar 27  Quantum key distribution: First step (distributing Bell pairs). Bell test. Measuring the raw key. Minentropy.  Bell, TildeNotation, BellTest, BellTestAna, RawKey, RawKeyKeyDiff, RawKeyGuess, MinEnt, RawKeyEnt, RawKeyAna  Video, Whiteboard 
Mar 28  Measuring the key with t errors. Equivalence of the alternative QKD security definition.  QKDSecDef, RawKeyGuess  Whiteboard 
Apr 03  Error correcting codes. Error correction step in QKD. Strong randomness extractors. Universal hash functions. Privacy amplification in QKD. Finished QKD security proof.  ECC, QKDCorr, Chain, QKDCorrAna, PrivAmp, RandExtQ, UHF, LHL, PrivAmpAna, QKDWrapup  Video, Whiteboard 
Apr 04  Last bit of key deleted or set 0. Error correction after randomness extraction. Extracting too much from a key. Problems with deterministic randomness extractors. Lattices (briefly). The SIS hash function.  ECC, RandExtC, UHF  Whiteboard 
Apr 10  Shor's algorithm. Period finding. Factoring. Discrete logarithm.  Fact, Period, FactFromPeriod, DFT, DFTAlgo, Shor  Video, Whiteboard 
Apr 11  Using period finding to solve discrete logarith. Implementing the Quantum Fourier Transform.  DFTAlgo  Whiteboard 
Apr 17  LWE problem (computational and decisional). Regev's cryptosystem. INDCPA security of Regev's cryptosystem.  BinCompLWE, CompLWE, DecLWE, Regev, RegevCPA  Video, Whiteboard 
Apr 18  Example of Regev's cryptosystem. Solving SVP using SIS. Using a short basis to make a trapdoor.  Regev  Whiteboard 
Apr 24  INDCCA security. KEMs and hybrid encryption. FujisakiOkamoto transform.  IndCca, KEM, HybEnc, IndCcaKem, FO, FoSec  Video, Whiteboard 
Apr 25  Quantum random oracle model. Simplified FujisakiOkamoto example. O2H Theorem.  QromIdea, QromEx, O2H  Video, Whiteboard 
May 02  FO with implicit rejection. Applications of O2H. Semiclassical oracles. O2H on a set of inputs.  QromIdea, QromEx, O2H  Whiteboard 
May 08  Classical zeroknowledge proofs. Difficulty with rewinding in the quantum case.  ProofSys, ZK, GIZK, QZKProblem  Video, Whiteboard 
May 09  Aborting simulators  classical and quantum.  ProofSys, ZK, GIZK, QZK, QAbortSim  Whiteboard 
May 15  Quantum zeroknowledge. Difficulty with rewinding in the quantum case. Constructing a quantum ZK simulator.  QZK, QRewind, QZKAna  Video 
May 16  Zero Knowledge: Encryption input protocol, Hamiltonian cycles protocol  ProofSys, ZK, GIZK, QZK  Whiteboard 
May 22  Schrödinger equation. Particle in an infinite potential well.  Physical  Video, Whiteboard 
Out  Due  Homework  Solution 

20230213  20230220  Homework 1  Solution 1 
20230220  20230227  Homework 2  Solution 2 
20230227  20230306  Homework 3  Solution 3 
20230306  20230313  Homework 4  Solution 4 
20230313  20230320  Homework 5  Solution 5 
20230320  20230327  Homework 6  Solution 6 
20230327  20230403  Homework 7  Solution 7 
20230403  20230410  Homework 8  Solution 8 
20230410  20230417  Homework 9  Solution 9 
20230417  20230424  Homework 10  Solution 10 
20230425  20230503  Homework 11  Solution 11 
20230508  20230515  Homework 12  Solution 12 
20230515  20230522  Homework 13 
In quantum cryptography we use quantum
mechanical effects to construct secure protocols. The paradoxical
nature of quantum mechanics allows for constructions that solve
problems known to be impossible without quantum mechanics. This lecture
gives an introduction into this fascinating area.
Possible topics include:
You need no prior knowledge of quantum mechanics. You should have heard some introductory lecture on cryptography. You should enjoy math and have a sound understanding of linear algebra.
[NC00] Nielsen, Chuang. "Quantum Computation and Quantum Information" Cambridge University Press, 2000. A standard textbook on quantum information and quantum computing. Also contains some quantum cryptography.
Further
reading may be suggested during the
course. See the "further reading" paragraphs in the lecture notes.